Question: Can this differential equation be solved using separation of variables? $\dfrac{dy}{dx}=\sqrt{3xy+5y}$ Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Answer: For an equation to be solvable using separation of variables, we need to be able to bring it to the form $\dfrac{dy}{dx}=f(x)g(y)$. In this form, $f(x)$ doesn't include $y$ and $g(y)$ doesn't include $x$. Notice that we must multiply, not add, $f(x)$ and $g(y)$. First, let's factor $\sqrt{3xy+5y}$ as $\sqrt{3x+5}\cdot\sqrt{y}$. Now, let $f(x)=\sqrt{3x+5}$ and $g(y)=\sqrt{y}$. Our equation is indeed in the form $\dfrac{dy}{dx}=f(x)g(y)$. Yes, the equation can be solved using separation of variables.